1. The problem statement, all variables and given/known data Prove that similar matrices have the same rank. 2. Relevant equations 3. The attempt at a solution Similar matrices are related via: B = P-1AP, where B, A and P are nxn matrices.. since P is invertible, it rank(P) = n, and so since the main diagonal of P all > 0, multiplying by P will not change the rank of A, so rank B = rank A. Is that seem right?